The formula to calculate the critical fiber length is:
\[ l_c = \frac{\sigma_f \cdot d}{2 \cdot \tau_c} \]
Where:
Critical fiber length is the length necessary for effective strengthening and stiffening of the composite material.
Tensile strength of fiber refers to the maximum stress a material can withstand while being stretched or pulled before breaking.
Fiber diameter refers to the width or diameter of the individual fibers within a material, such as in composite materials or textiles.
Critical shear stress is either the fiber matrix bond strength or the shear yield stress of the matrix, whichever is lower.
Let's assume the following values:
Using the formula:
\[ l_c = \frac{6375000 \cdot 0.01}{2 \cdot 3010000} = 0.0105897009966777 \text{ m} \]
The critical fiber length is 0.0105897009966777 meters.
| Tensile Strength (Pa) | Fiber Diameter (m) | Critical Shear Stress (Pa) | Critical Fiber Length (m) |
|---|---|---|---|
| 6000000 | 0.005 | 2500000 | 0.0060000000 |
| 6000000 | 0.005 | 3000000 | 0.0050000000 |
| 6000000 | 0.005 | 3500000 | 0.0042857143 |
| 6000000 | 0.01 | 2500000 | 0.0120000000 |
| 6000000 | 0.01 | 3000000 | 0.0100000000 |
| 6000000 | 0.01 | 3500000 | 0.0085714286 |
| 6000000 | 0.015 | 2500000 | 0.0180000000 |
| 6000000 | 0.015 | 3000000 | 0.0150000000 |
| 6000000 | 0.015 | 3500000 | 0.0128571429 |
| 6500000 | 0.005 | 2500000 | 0.0065000000 |
| 6500000 | 0.005 | 3000000 | 0.0054166667 |
| 6500000 | 0.005 | 3500000 | 0.0046428571 |
| 6500000 | 0.01 | 2500000 | 0.0130000000 |
| 6500000 | 0.01 | 3000000 | 0.0108333333 |
| 6500000 | 0.01 | 3500000 | 0.0092857143 |
| 6500000 | 0.015 | 2500000 | 0.0195000000 |
| 6500000 | 0.015 | 3000000 | 0.0162500000 |
| 6500000 | 0.015 | 3500000 | 0.0139285714 |
| 7000000 | 0.005 | 2500000 | 0.0070000000 |
| 7000000 | 0.005 | 3000000 | 0.0058333333 |
| 7000000 | 0.005 | 3500000 | 0.0050000000 |
| 7000000 | 0.01 | 2500000 | 0.0140000000 |
| 7000000 | 0.01 | 3000000 | 0.0116666667 |
| 7000000 | 0.01 | 3500000 | 0.0100000000 |
| 7000000 | 0.015 | 2500000 | 0.0210000000 |
| 7000000 | 0.015 | 3000000 | 0.0175000000 |
| 7000000 | 0.015 | 3500000 | 0.0150000000 |